Another important motivation for the study of the \(T\bar{T}\)  deformation comes from the theory of integrable models. It is by now known that for integrable models and CFTs, the \(T\bar{T}\)  deformation is a special case of a more general family of integrable deformations triggered by bilinear operators. Such integrable bilinear deformations lead to a novel type of integrable models. For relativistic integrable QFT and CFT, more general solvable bilinear deformations with an additional \(U(1)\)  current have been studied in [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. Deformations involving higher conserved currents have been proposed and studied in [9]}, [10]}, [11]}, [12]}, [13]}. For spin chains, similar deformations have been introduced even before the \(T\bar{T}\)  deformations in [14]}, [15]} and are called bilocal deformations, cf. Table REF .
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